Does the following series converge or diverge?

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Does the following series converge or diverge?

Mathematics
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\[\sum_{n=2}^{infinity} 1/n \sqrt{\ln(n)}\]
I'm wanting to say it converges to 1, but I'm not sure how to prove that. Real analysis wasn't my strong point.
do you know what test to use?

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my original thought was ratio, but i dont know how to apply that here
I'm wanting to say it has something to do with the Cauchy Criterion
...I have no idea what that means..haha
I don't think we covered that
Oh, the ratio test should work.
really? Let me try that really quickly
Well, that gave me infinity over infinity...maybe i'm doing it wrong?
Looking up properties of the natural log right now, give me a sec.
thanks so much!
Integral test would be easier since i see ln(n) and 1/n there.
oh that makes sense!
Ok all i can think of is that \[n / (n+1) \le 1\] and \[\sqrt(\ln(n+1)) \le n\] and \[\sqrt(\ln(n)) \le n\] thus \[\left| n/(n+1) * \sqrt(\ln(n+1)) / \sqrt(\ln(n)) \right| \le \left| 1 * n/n \right| \le 1\]
hmm. Ok, let me think about that for a min :)
hmm actually that might not work cause the ration needs to be less than 1 for the ratio test to work
when i worked it doing the integral test i got infinity meaning divergent does that seem right?

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